If this is a typical Betta tank without a filter, then you will not cycle. You will change water every day, maybe every other day, depending on the size Betta bowl.

Here is a google hit on cycling: http://faq.thekrib.com/begin-cycling.html
If you choose to keep anything other than your most basic Betta bowl, understanding the Nitrogen Cycle is essential. This is the first thing you should learn about fish, even more important that what fish food to buy.

A post closer to home on cycling is here http://www.fishforum.com/viewtopic.php?t=3738
No matter where you get the info, the process is about the same. The tank you have is now set up to start a "fishy" cycle since you have a fish in it. It will make a difference how you need to approach it.